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recognition so promptly accorded him, he could not refrain
from casting a backward glance over his career. Years later,
thinking of the happiness of the occasion and of what that
occasion had opened up for him when he was forty years of age,
he remarked sadly that 'everything hi life comes too late.*
Weierstrass did not return to Braunsberg. No really suitable
position being open at the time, the leading German mathema-
ticians did what they could to tide over the emergency and got
Weierstrass appointed Professor of Mathematics at the Royal
Polytechnic School in Berlin. This appointment dated from
1 July 1856; in the autumn of the same year he was made
Assistant Professor (in addition to the other post) at the Uni-
versity of Berlin and was elected to the Berlin Academy.
The excitement of novel working conditions and the strain
of too much lecturing presently brought on a nervous break-
down. Weierstrass had also been overworking at his researches.
In the summer of 1859 he was forced to abandon his course and
take a rest cure. Returning in the autumn he continued his work,
apparently refreshed, but in the following March was suddenly
attacked by spells of vertigo, and he collapsed in the middle of
a lecture.
All the rest of his life he was bothered with the same trouble
off and on, and after resuming his work - as full professor, with
a considerably lightened load - never trusted himself to write
Ms own formulae on the board. His custom was to sit where he
could see the class and the blackboard, and dictate to some
student delegated from the class what was to be written. One
of these 'mouthpieces' of the master developed a rash propen-
sity to try to improve on what he had been told to write.
Weierstrass would reach up and rub out the amateur's efforts
and make him write what he had been told. Occasionally the
battle between the professor and the obstinate student would
go to several rounds, but in the end Weierstrass always won.
He had seen little boys misbehaving before.
As the fame of his work spread over Europe (and later to
America), Weierstrass' classes began to grow rather unwieldy
and he would sometimes regret that the quality of his auditors
lagged far behind their rapidly mounting quantity* Nevertbe-